finding the max or min of a quadratic function

label Algebra
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answer the questions below about the quadratic function

g(x)=x²+8+18

a. does the function have a minimum or maximum value

b. what is the function's min or max value

c. where does it occur  x=

Oct 10th, 2015

Thank you for the opportunity to help you with your question!

g(x)=x²+8x+18

NB I am assuming that you erroneously ignored the x in 8x.

a.

To determine whether the function has a maximum or minimum, we differentate it twice i.e

first derivative, g'(x) = 2x+8

Second derivative, g"(x) = 2

Therefore the function has a minimum point since the second derivative is positive i.e (+2)


b.

The function minimum point is the point where the slope/gradient of the function is equal to zero.

The slope/gradient of the function is given by the first derivative

Therefore, g'(x) = 2x+8 = 0 

2x =-8 hence x=-4

Substituting the value of X into the equation gives

g(x) = (-4)^2+8(-4)+18 = 2

Therefore the functions minimum point is 2

c.

As calculated above, the function's minimum point occurs at the point where x= -4


Let me know if my assumption of instituting x into the function was right or wrong.Regards.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 10th, 2015

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